A model of coupled mantle convection and planetary tectonics is used to demonstrate that history dependence can outweigh the effects of a planet's energy content and material parameters in determining its tectonic state. The mantle convection-surface tectonics system allows multiple tectonic modes to exist for equivalent planetary parameter values. The tectonic mode of the system is then determined by its specific geologic and climatic history. This implies that models of tectonics and mantle convection will not be able to uniquely determine the tectonic mode of a terrestrial planet without the addition of historical data. Historical data exists, to variable degrees, for all four terrestrial planets within our solar system. For the Earth, the planet with the largest amount of observational data, debate does still remain regarding the geologic and climatic history of Earth's deep past but constraints are available. For planets in other solar systems, no such constraints exist at present. The existence of multiple tectonic modes, for equivalent parameter values, points to a reason why different groups have reached different conclusions regarding the tectonic state of extrasolar terrestrial planets larger than Earth ("super-Earths"). The region of multiple stable solutions is predicted to widen in parameter space for more energetic mantle convection (as would be expected for larger planets). This means that different groups can find different solutions, all potentially viable and stable, using identical models and identical system parameter values. At a more practical level, the results argue that the question of whether extrasolar terrestrial planets will have plate tectonics is unanswerable and will remain so until the temporal evolution of extrasolar planets can be constrained.
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